getMomentumFlowLines

Description

The stress-energy tensor momentum flux components structure can be visualized by treating the values as a vector field and creating paths along the field.

Momentum Flowlines

The momentum flow field $\Omega^\mu$is constructed from the given stress-energy tensor as:

$\Omega^\mu(X) = \left(T^{01}(X), T^{02}(X), T^{03}(X)\right)$

Method

The flowlines are found by forward-stepping trajectories through the vector field of the momentum flux components. This currently assumes a static stress-energy tensor without time variation, where the timesteps of the flowlines are a virtual timestep, not a step through the time slices of the stress-energy tensor. Newton's method is used to solve the steps.

Syntax

[paths] = getMomentumFlowLines(energyTensor, startPoints, stepSize, maxSteps, ScaleFactor)

Input Arguments

blue are required inputs.

orange are optional inputs with native default values.

Inputs	Format	Type	Description
energyTensor	struct	object	Input stress-energy tensor.
startPoints	1x3 cell of 1xN array	double	Starting locations for the flowlines, are given as {x, y, z} points on the spatial hypersurface (3D coordinates). The points for each cell are in the 1 x N array. Each cell should have a 1 x N array of the same size N.
stepSize	1x1 array	double	The step size that is used in the forward step of the Newton solver.
ScaleFactor	1x1 array	double	Scales the value of the momentum flux components.

Output Arguments

Outputs	Format	Type	Description
paths	1x3 cell of 1xN array	double	Returns each path as a new cell index with an array of vectors for each 3D coordinate of the flowline path up to the max step (N < maxSteps). Note that if the path reaches world boundaries the flowline is terminated.